Estimated Parameters of Exponential Smoothing | |
Parameter | Value |
alpha | 0.0219538867872071 |
beta | 0.849748700445273 |
gamma | 0.31528236748219 |
Interpolation Forecasts of Exponential Smoothing | |||
t | Observed | Fitted | Residuals |
13 | 2564 | 2540.43602621567 | 23.5639737843312 |
14 | 2820 | 2786.89098463547 | 33.1090153645282 |
15 | 3508 | 3455.56989823856 | 52.4301017614375 |
16 | 3088 | 3050.56973081324 | 37.4302691867629 |
17 | 3299 | 3283.39819595327 | 15.6018040467293 |
18 | 2939 | 2961.14590175454 | -22.1459017545403 |
19 | 3320 | 3366.75875814298 | -46.7587581429775 |
20 | 3418 | 3100.59931681039 | 317.400683189611 |
21 | 3604 | 3599.56837945171 | 4.43162054829372 |
22 | 3495 | 3694.90035916793 | -199.900359167934 |
23 | 4163 | 4546.02210889468 | -383.022108894679 |
24 | 4882 | 5493.2020492742 | -611.202049274198 |
25 | 2211 | 2599.88516127479 | -388.885161274794 |
26 | 3260 | 2829.75306104031 | 430.246938959695 |
27 | 2992 | 3514.04923030427 | -522.049230304274 |
28 | 2425 | 3070.94469955403 | -645.944699554028 |
29 | 2707 | 3249.40172859017 | -542.401728590168 |
30 | 3244 | 2870.35214456770 | 373.647855432297 |
31 | 3965 | 3232.17887781673 | 732.821122183275 |
32 | 3315 | 3080.69145459866 | 234.308545401342 |
33 | 3333 | 3443.40913219231 | -110.409132192313 |
34 | 3583 | 3446.36955696997 | 136.630443030027 |
35 | 4021 | 4185.26716669707 | -164.267166697068 |
36 | 4904 | 4995.02349954517 | -91.0234995451665 |
37 | 2252 | 2332.71711674191 | -80.7171167419096 |
38 | 2952 | 2791.13887019654 | 160.861129803455 |
39 | 3573 | 3144.28423347904 | 428.715766520959 |
40 | 3048 | 2716.65581452568 | 331.34418547432 |
41 | 3059 | 2963.79533803315 | 95.2046619668545 |
42 | 2731 | 2920.88139677717 | -189.881396777173 |
43 | 3563 | 3399.23070619969 | 163.769293800309 |
44 | 3092 | 3106.31236676567 | -14.3123667656746 |
45 | 3478 | 3367.92849927736 | 110.07150072264 |
46 | 3478 | 3470.47216221219 | 7.52783778780577 |
47 | 4308 | 4130.19080414777 | 177.809195852225 |
48 | 5029 | 5002.94381004437 | 26.0561899556269 |
49 | 2075 | 2341.88088511256 | -266.880885112562 |
50 | 3264 | 2893.34757275042 | 370.652427249584 |
51 | 3308 | 3364.69995854097 | -56.6999585409685 |
52 | 3688 | 2896.39343174623 | 791.60656825377 |
53 | 3136 | 3106.59651997808 | 29.4034800219247 |
54 | 2824 | 2987.66349368554 | -163.663493685535 |
55 | 3644 | 3624.47889309474 | 19.5211069052552 |
56 | 4694 | 3273.89766748418 | 1420.10233251582 |
57 | 2914 | 3673.86917067579 | -759.869170675788 |
58 | 3686 | 3763.76039016466 | -77.760390164658 |
59 | 4358 | 4570.98991837248 | -212.989918372482 |
60 | 5587 | 5498.17264158295 | 88.8273584170529 |
61 | 2265 | 2496.17060320570 | -231.170603205705 |
62 | 3685 | 3347.35915372792 | 337.640846272082 |
63 | 3754 | 3747.33898683811 | 6.66101316189406 |
64 | 3708 | 3539.20744667407 | 168.792553325934 |
65 | 3210 | 3504.03572867123 | -294.035728671233 |
66 | 3517 | 3298.69945035517 | 218.300549644833 |
67 | 3905 | 4100.03008792936 | -195.030087929355 |
68 | 3670 | 4190.1011634476 | -520.1011634476 |
69 | 4221 | 3806.95905597092 | 414.040944029085 |
70 | 4404 | 4159.40935432775 | 244.590645672249 |
71 | 5086 | 5015.05920873687 | 70.9407912631259 |
72 | 5725 | 6160.50026357569 | -435.500263575693 |
73 | 2367 | 2694.56000863673 | -327.560008636734 |
74 | 3819 | 3825.67730976688 | -6.67730976687517 |
75 | 4067 | 4131.41753902044 | -64.4175390204364 |
76 | 4022 | 3939.85923129124 | 82.1407687087567 |
77 | 3937 | 3725.88583305532 | 211.11416694468 |
78 | 4365 | 3679.12360994954 | 685.876390050455 |
79 | 4290 | 4429.40676732055 | -139.406767320545 |
Extrapolation Forecasts of Exponential Smoothing | |||
t | Forecast | 95% Lower Bound | 95% Upper Bound |
80 | 4422.69523593488 | 4191.14601114111 | 4654.24446072865 |
81 | 4343.32522124694 | 4110.12578300933 | 4576.52465948454 |
82 | 4668.34678357059 | 4430.88942459568 | 4905.8041425455 |
83 | 5544.839680593 | 5296.0800743669 | 5793.59928681909 |
84 | 6629.07501932279 | 6356.60615170544 | 6901.54388694014 |
85 | 2859.88705468780 | 2615.75914260311 | 3104.01496677250 |
86 | 4241.30154429076 | 3969.00497576137 | 4513.59811282014 |
87 | 4575.15167462803 | 4278.008072942 | 4872.29527631407 |
88 | 4428.69191307064 | 4114.4905308867 | 4742.89329525458 |
89 | 4244.56764548917 | 3914.14174975514 | 4574.9935412232 |
90 | 4357.91690051763 | 3997.35064722494 | 4718.48315381033 |
91 | 4886.56018785983 | 4536.78910148962 | 5236.33127423003 |